Let $Sset$ denote the category of simplicial sets with its Quillen model structure,
when is a functor $F: (ho Sset)^{op} \to Ab$ representable? With $Ab$ category of Abelian groups. There is probably some classical references but my googlefu wasn't strong enough. I am hoping it would just be the direct translation of Brown representability theorem for $Ab$ valued cofunctors on $hoTop$.